Prescribed-time Tracking Control of Hypersonic Vehicles by Time-varying High-gain Feedback
-
摘要: 研究了高超声速飞行器控制通道存在未知环境干扰时的指定时间跟踪控制问题. 基于高超声速飞行器的输入输出线性化模型, 借助参量 Lyapunov方程的一些性质, 设计一种光滑、有界的时变高增益控制律. 相比于现有的高超声速飞行器有限/固定时间控制方法, 该算法不会出现抖振现象, 同时收敛时间不依赖于初始状态且可以事先设定. 当高超声速飞行器存在未知的有界环境匹配干扰时, 该控制器能使高度和速度在指定时间跟踪上参考信号. 仿真结果验证了方法的有效性.Abstract: The prescribed-time tracking control problem of hypersonic vehicles in the presence of unknown environmental disturbances in the control channel is studied. Based on the input-output linearization model of hypersonic vehicles and some properties of a parametric Lyapunov equation, a smooth and bounded time-varying high-gain controller is proposed. Compared with the existing finite/fixed time control methods for hypersonic vehicles, the chattering phenomenon does not appear in the algorithm, and the convergence time does not depend on the initial state and can be set in advance. When the hypersonic vehicle has unknown bounded environmental matched disturbance, the proposed controller can ensure that the altitude and velocity track the reference signals in the prescribed time. Finally, simulation results verify the effectiveness of the proposed method.
-
图 1 速度、飞行航迹角、高度和攻角变化曲线
Fig. 1 The curves of changes in velocity, flight path angle, altitude and angle of attack
图 2 俯仰角速率、发动机节流阀开度及其导数变化曲线
Fig. 2 The curves of changes in pitch rate, engine throttle setting and their time-derivative
图 4 速度误差及其导数变化曲线
Fig. 4 The curves of changes in velocity errors and their time-derivatives
图 5 高度误差及其导数变化曲线
Fig. 5 The curves of changes in altitude errors and their time-derivatives
表 1 高超声速飞行器参数以及飞行环境参数
Table 1 The parameters of the hypersonic vehicle and the flight environment
模型参数 符号 值 质量 $m$ 136817.841 kg 地球半径 $R_{{\rm{e}}}$ 6371386.8 m 参考面积 $S$ 334.729653 m2 平均气动弦长 $\bar{c}$ 80 升降副翼弦长 $c_{{\rm{e}}}$ 0.029 2 绕$ y $轴的转动惯量 $ I_{yy} $ 9.4907 × 106 kg$\cdot\; {\rm{m} }^2$ 空气密度 $\rho$ 0.0125 kg/m3 重力常数 $\mu $ 3.9360 × 1014 m3/s2 
下载: 导出CSV
-
[1] Hu Q L, Meng Y, Wang C L, Zhang Y M. Adaptive backstepping control for air-breathing hypersonic vehicles with input nonlinearities. Aerospace Science and Technology, 2018, 73: 289−299 doi: 10.1016/j.ast.2017.12.001 [2] 孙长银, 穆朝絮, 余瑶. 近空间高超声速飞行器控制的几个科学问题研究. 自动化学报, 2013, 39(11): 1901−1913 doi: 10.3724/SP.J.1004.2013.01901Sun Chang-Yin, Mu Chao-Xu, Yu Yao. Some control problems for near space hypersonic vehicles. Acta Automatica Sinica, 2013, 39(11): 1901−1913 doi: 10.3724/SP.J.1004.2013.01901 [3] Hu X X, Wu L G, Hu C H, Gao H J. Fuzzy guaranteed cost tracking control for a flexible air-breathing hypersonic vehicle. IET Control Theory and Applications, 2012, 6(9): 1238−1249 [4] Xu H J, Mirmirani M D, Ioannou P A. Adaptive sliding mode control design for a hypersonic flight vehicle. Journal of Guidance, Control, and Dynamics, 2004, 27(5): 829−838 doi: 10.2514/1.12596 [5] Wang Q, Stengel R F. Robust nonlinear control of a hypersonic aircraft. Journal of Guidance, Control, and Dynamics, 2000, 23(1): 15−26 [6] Zong Q, Wang J, Tao Y. Adaptive high-order dynamic sliding mode control for a flexible air-breathing hypersonic vehicle. International Journal of Robust and Nonlinear Control, 2013, 23(15): 1718−1736 doi: 10.1002/rnc.3040 [7] Mu C X, Zong Q, Tian B L, Xu W. Continuous sliding mode controller with disturbance observer for hypersonic vehicles. IEEE/CAA Journal of Automatica Sinica, 2015, 2(1): 45−55 doi: 10.1109/JAS.2015.7032905 [8] Mu C X, Ni Z, Sun C Y, He H B. Air-breathing hypersonic vehicle tracking control based on adaptive dynamic programming. IEEE Transactions on Neural Networks and Learning Systems, 2016, 28(3): 584−598 [9] Sun H B, Li S H, Sun C Y. Finite time integral sliding mode control of hypersonic vehicles. Nonlinear Dynamics, 2013, 73(1): 229−244 [10] Bhat S P, Bernstein D S. Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization, 2000, 38(3): 751−766 doi: 10.1137/S0363012997321358 [11] 丁世宏, 李世华. 有限时间控制问题综述. 控制与决策, 2011, 26(2): 161−169Ding Shi-Hong, Li Shi-Hua. A survey for finite-time control problems. Control and Decision, 2011, 26(2): 161−169 [12] 刘洋, 井元伟, 刘晓平, 李小华. 非线性系统有限时间控制研究综述. 控制理论与应用, 2020, 37(1): 1−12 doi: 10.7641/CTA.2019.90351Liu Yang, Jing Yuan-Wei, Liu Xiao-Ping, Li Xiao-Hua. Survey on finite-time control for nonlinear systems. Control Theory and Applications, 2020, 37(1): 1−12 doi: 10.7641/CTA.2019.90351 [13] 张檬, 韩敏. 基于单向耦合法的不确定复杂网络间有限时间同步. 自动化学报, 2021, 47(7): 1624−1632Zhang Meng, Han Min. Finite-time synchronization between uncertain complex networks based on unidirectional coupling method. Acta Automatica Sinica, 2021, 47(7): 1624−1632 [14] 李小华, 胡利耀. 一类$p$规范型非线性系统预设性能有限时间$H_{\infty}$跟踪控制. 自动化学报, 2021, 47(12): 2870−2880Li Xiao-Hua, Hu Li-Yao. Prescribed performance finite-time $H_{\infty}$ tracking control for a class of $p{\text{-}}{\rm{normal}}$ form nonlinear systems. Acta Automatica Sinica, 2021, 47(12): 2870−2880 [15] 孙经广, 宋申民, 陈海涛, 李学辉. 高超声速飞行器有限时间饱和跟踪控制. 控制理论与应用, 2017, 34(10): 1349−1360 doi: 10.7641/CTA.2017.60705Sun Jing-Guang, Song Shen-Min, Chen Hai-Tao, Li Xue-Hui. Finite-time tracking control of the hypersonic vehicle with input saturation. Control Theory and Applications, 2017, 34(10): 1349−1360 doi: 10.7641/CTA.2017.60705 [16] Wang X, Guo J, Tang S J, Qi S. Fixed-time disturbance observer based fixed-time backstepping control for an air-breathing hypersonic vehicle. ISA Transactions, 2019, 88: 233−245 doi: 10.1016/j.isatra.2018.12.013 [17] Kwon W, Pearson A. A modified quadratic cost problem and feedback stabilization of a linear system. IEEE Transactions on Automatic Control, 1977, 22(5): 838−842 doi: 10.1109/TAC.1977.1101619 [18] Rekasius Z. An alternate approach to the fixed terminal point regulator problem. IEEE Transactions on Automatic Control, 1964, 9(3): 290−292 doi: 10.1109/TAC.1964.1105700 [19] Zarchan P. Tactical and Strategic Missile Guidance. Washington DC: AIAA Inc, 2012. 11−28 [20] Song Y D, Wang Y J, Holloway J, Krstic M. Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time. Automatica, 2017, 83: 243−251 doi: 10.1016/j.automatica.2017.06.008 [21] Zhou B. Finite-time stabilization of linear systems by bounded linear time-varying feedback. Automatica, 2020, 113: Article No. 108760 doi: 10.1016/j.automatica.2019.108760 [22] Zhou B. Finite-time stability analysis and stabilization by bounded linear time-varying feedback. Automatica, 2020, 121: Article No. 109191 doi: 10.1016/j.automatica.2020.109191 [23] Sun J G, Xu S L, Song S M, Dong X J. Finite-time tracking control of hypersonic vehicle with input saturation. Aerospace Science and Technology, 2017, 71: 272−284 doi: 10.1016/j.ast.2017.09.036 [24] Yin X M, Wang B, Liu L, Wang Y J. Disturbance observer-based gain adaptation high-order sliding mode control of hypersonic vehicles. Aerospace Science and Technology, 2019, 89: 19−30 doi: 10.1016/j.ast.2019.03.030 [25] Slotine J J, Sastry S S. Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators. International Journal of Control, 1983, 38(2): 465−492 doi: 10.1080/00207178308933088 [26] 高为炳. 变结构控制的理论及设计方法. 北京: 科学出版社, 1996. 21−40Gao Wei-Bing. Theory and Design Method of Variable Structure Control. Beijing: Science Press, 1996. 21−40 [27] Levant A. Sliding order and sliding accuracy in sliding mode control. International Journal of Control, 1993, 58(6): 1247−1263 doi: 10.1080/00207179308923053 [28] Xu J X, Lee T H, Wang M, Yu X H. Design of variable structure controllers with continuous switching control. International Journal of Control, 1996, 65(3): 409−431 doi: 10.1080/00207179608921704 [29] Wong L K, Leung F H F, Tam P K S. A chattering elimination algorithm for sliding mode control of uncertain non-linear systems. Mechatronics, 1998, 8(7): 765−775 doi: 10.1016/S0957-4158(98)00031-2 [30] An H, Wu Q Q, Wang C H. Differentiator based full-envelope adaptive control of air-breathing hypersonic vehicles. Aerospace Science and Technology, 2018, 82: 312−322 [31] Zhou B. On asymptotic stability of linear time-varying systems. Automatica, 2016, 68: 266−276 doi: 10.1016/j.automatica.2015.12.030 [32] Khalil H K. Nonlinear Systems (3rd ed.). Englewood Cliffs: Prentice-Hall, 2002. 102−103 [33] Ding Y B, Wang X G, Bai Y L, Cui N G. Adaptive higher order super-twisting control algorithm for a flexible air-breathing hypersonic vehicle. Acta Astronautica, 2018, 152: 275−288 doi: 10.1016/j.actaastro.2018.08.010 [34] Parker J T, Serrani A, Yurkovich S, Bolender M A, Doman D B. Control-oriented modeling of an air-breathing hypersonic vehicle. Journal of Guidance, Control, and Dynamics, 2007, 30(3): 856−869 doi: 10.2514/1.27830 [35] Zhou B, Shi Y. Prescribed-time stabilization of a class of nonlinear systems by linear time-varying feedback. IEEE Transactions on Automatic Control, 2021, 66(12): 6123−6130 doi: 10.1109/TAC.2021.3061645 -
图(5) / 表(1)
计量
- 文章访问数: 799
- HTML全文浏览量: 420
- PDF下载量: 242
- 被引次数: 0
